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On the tautological rings of stacks of twisted curves

Hsian-Hua Tseng

Abstract

We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.

On the tautological rings of stacks of twisted curves

Abstract

We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.
Paper Structure (14 sections, 5 theorems, 37 equations)

This paper contains 14 sections, 5 theorems, 37 equations.

Table of Contents

  1. Introduction
  2. Backgroud
  3. This paper
  4. Outlook
  5. Acknowledgment
  6. Definitions of tautological rings
  7. Chow rings
  8. Tautological rings
  9. Stratum classes
  10. An additive spanning set of tautological rings
  11. Closure under intersection product
  12. Closure under pushforwards
  13. Gluing maps
  14. Forgetful maps

Key Result

Lemma 1.3

$\mathfrak{Z}_{g,I,m}^{tw,triv}$ is closed. The composition of the inclusion and the natural map defines an isomorphism

Theorems & Definitions (11)

  • Example 1.1
  • Definition 1.2
  • Lemma 1.3
  • Corollary 1.4
  • Definition 1.5
  • Definition 1.6
  • Definition 1.7: Decorated stratum classes
  • Theorem 2.1
  • Definition 2.2
  • Proposition 2.3
  • ...and 1 more